Simplify; express your answer in exponential form. Assume $q\neq 0, p\neq 0$. $\dfrac{{(q^{5}p^{-4})^{-4}}}{{(q^{-4}p^{-1})^{3}}}$
To start, try simplifying the numerator and the denominator independently. In the numerator, we can use the distributive property of exponents. ${(q^{5}p^{-4})^{-4} = (q^{5})^{-4}(p^{-4})^{-4}}$ On the left, we have ${q^{5}}$ to the exponent ${-4}$ . Now ${5 \times -4 = -20}$ , so ${(q^{5})^{-4} = q^{-20}}$ Apply the ideas above to simplify the equation. $\dfrac{{(q^{5}p^{-4})^{-4}}}{{(q^{-4}p^{-1})^{3}}} = \dfrac{{q^{-20}p^{16}}}{{q^{-12}p^{-3}}}$ Break up the equation by variable and simplify. $\dfrac{{q^{-20}p^{16}}}{{q^{-12}p^{-3}}} = \dfrac{{q^{-20}}}{{q^{-12}}} \cdot \dfrac{{p^{16}}}{{p^{-3}}} = q^{{-20} - {(-12)}} \cdot p^{{16} - {(-3)}} = q^{-8}p^{19}$